The numerical study presented in this work describes the direct and inverse mixed convection problems in a slot-ventilated enclosure subjected to an unknown heat flux on one side. Particularly, the interaction of internal natural convection with the cold ventilated flow leads to various flow fields depending on the Richardson number, Reynolds number, and the functional form of the imposed boundary heat flux. Fluid and heat transport structures across the enclosure are visualized by the streamlines and heatlines, respectively. Subsequently, an iterative conjugate gradient method is applied such that the gradient of the cost function is introduced when the appropriate sensitivity and adjoint problems are defined for a domain of arbitrary geometries. In this approach, no a priori information is needed about the unknown boundary heat fluxes to be determined. The accuracy of the heat flux profile solutions is shown to depend strongly on the values of Reynolds number and flux functional forms. Effects of measurement errors on the accuracy of estimation are also investigated. The present work is significant for the flow control simultaneously involving the natural convection and forced convection. (C) 2009 Elsevier Ltd. All rights reserved.